Coupled KdV equations derived from atmospherical dynamics

Some types of coupled Korteweg de-Vries (KdV) equations are derived from an atmospheric dynamical system. In the derivation procedure, an unreasonable $y$-average trick (which is usually adopted in literature) is removed. The derived models are classified via Painlev\'e test. Three types of $\tau$-function solutions and multiple soliton solutions of the models are explicitly given by means of the exact solutions of the usual KdV equation. It is also interesting that for a non-Painlev\'e integrable coupled KdV system there may be multiple soliton solutions.Comment: 19 pages, 2 figure

Distribution of Spectral Lags in Gamma Ray Bursts

Using the data acquired in the Time To Spill (TTS) mode for long gamma-ray bursts (GRBs) collected by the Burst and Transient Source Experiment on board the Compton Gamma Ray Observatory (BATSE/CGRO), we have carefully measured spectral lags in time between the low (25-55 keV) and high (110-320 keV) energy bands of individual pulses contained in 64 multi-peak GRBs. We find that the temporal lead by higher-energy gamma-ray photons (i.e., positive lags) is the norm in this selected sample set of long GRBs. While relatively few in number, some pulses of several long GRBs do show negative lags. This distribution of spectral lags in long GRBs is in contrast to that in short GRBs. This apparent difference poses challenges and constraints on the physical mechanism(s) of producing long and short GRBs. The relation between the pulse peak count rates and the spectral lags is also examined. Observationally, there seems to be no clear evidence for systematic spectral lag-luminosity connection for pulses within a given long GRB.Comment: 20 pages, 4 figure

A Model for the Moving `Wisps' in the Crab Nebula

I propose that the moving `wisps' near the center of the Crab Nebula result from nonlinear Kelvin-Helmholtz instabilities in the equatorial plane of the shocked pulsar wind. Recent observations suggest that the wisps trace out circular wavefronts in this plane, expanding radially at speeds approximately less than c/3. Instabilities could develop if there is sufficient velocity shear between a faster-moving equatorial zone and a slower moving shocked pulsar wind at higher latitudes. The development of shear could be related to the existence of a neutral sheet -- with weak magnetic field -- in the equatorial zone, and could also be related to a recent suggestion by Begelman that the magnetic field in the Crab pulsar wind is much stronger than had been thought. I show that plausible conditions could lead to the growth of instabilities at the radii and speeds observed, and that their nonlinear development could lead to the appearance of sharp wisplike features.Comment: 7 pages; 3 postscript figures; LaTex, uses emulateapj.sty; to Appear in the Astrophysical Journal, Feb. 20, 1999, Vol. 51

Global axisymmetric stability analysis for a composite system of two gravitationally coupled scale-free discs

In a composite system of gravitationally coupled stellar and gaseous discs, we perform linear stability analysis for axisymmetric coplanar perturbations using the two-fluid formalism. The background stellar and gaseous discs are taken to be scale-free with all physical variables varying as powers of cylindrical radius $r$ with compatible exponents. The unstable modes set in as neutral modes or stationary perturbation configurations with angular frequency $\omega=0$.Comment: 7 pages using AAS styl

Spin injection from perpendicular magnetized ferromagnetic δ\delta-MnGa into (Al,Ga)As heterostructures

Electrical spin injection from ferromagnetic $\delta$-MnGa into an (Al,Ga)As p-i-n light emitting diode (LED) is demonstrated. The $\delta$-MnGa layers show strong perpendicular magnetocrystalline anisotropy, enabling detection of spin injection at remanence without an applied magnetic field. The bias and temperature dependence of the spin injection are found to be qualitatively similar to Fe-based spin LED devices. A Hanle effect is observed and demonstrates complete depolarization of spins in the semiconductor in a transverse magnetic field.Comment: 4 pages, 3 figure

Fast magnetohydrodynamic density waves in spiral galaxies

The newly observed large-scale structures of a southern grand-design spiral galaxy NGC 2997 in total and polarized radio-continuum emission together with their overall correlations with the known optical spiral structure are physically interpreted in terms of fast magnetohydrodynamic (MHD) density waves in contrast to slow MHD density waves in NGC 6946. The global spiral pattern of such fast MHD density waves extends from the very centre, where the disc rotates almost rigidly within ∼0.5 arcmin, all the way to the outer disc with a more or less flat rotation curve. To strengthen the case, several known features of spiral galaxies M51 and IC 342 are referred to and their pattern identifications discussed. It is emphasized that the nature of a magnetized spiral galaxy would be much better appreciated by examining large-scale structures in optical, atomic hydrogen H i, total and polarized radio-continuum and infrared emission together. As various star-formation processes occur concurrently and/or sequentially in spiral arms of high gas concentration, relatively broad and fuzzy H i arms, roughly coincident with optical arms in the inner disc, are expected to extend from the extremities of fading optical arms further into the outer gas disc. We predict that the south-east ‘magnetic arm', apparently isolated from any optical features, in total and polarized radio-continuum intensity maps of NGC 2997 should be associated with an H i gas arm yet to be detected in 21-cm line emissio

λϕ4\lambda\phi^4 model and Higgs mass in standard model calculated by Gaussian effective potential approach with a new regularization-renormalization method

Basing on new regularization-renormalization method, the $\lambda\phi^4$ model used in standard model is studied both perturbatively and nonperturbatively (by Gaussian effective potential). The invariant property of two mass scales is stressed and the existence of a (Landau) pole is emphasized. Then after coupling with the SU(2)$\times$U(1) gauge fields, the Higgs mass in standard model (SM) can be calculated as $m_H\approx$138GeV. The critical temperature ($T_c$) for restoration of symmetry of Higgs field, the critical energy scale ($\mu_c$, the maximum energy scale under which the lower excitation sector of the GEP is valid) and the maximum energy scale ($\mu_{max}$, at which the symmetry of the Higgs field is restored) in the standard model are $T_c\approx$476 GeV, $\mu_c\approx 0.547\times 10^{15}$GeV and $\mu_{\max}\approx 0.873 \times 10^{15}$ GeVv respectively.Comment: 12 pages, LaTex, no figur

New variable separation approach: application to nonlinear diffusion equations

The concept of the derivative-dependent functional separable solution, as a generalization to the functional separable solution, is proposed. As an application, it is used to discuss the generalized nonlinear diffusion equations based on the generalized conditional symmetry approach. As a consequence, a complete list of canonical forms for such equations which admit the derivative-dependent functional separable solutions is obtained and some exact solutions to the resulting equations are described.Comment: 19 pages, 2 fig